RUBIN, J.

Petitioner Monique B., the mother of minors Mariah T. and Bryce T., appeals from both the dependency court order taking jurisdiction over the children based on allegations of sexual and physical abuse (Welf. & Inst.Code, § 300, subds. (a), (b), (d), & (j)), and the dispositional order placing the children with their father. (Welf. & Inst.Code, § 361, subd. (c).) We affirm.

In February 2007, respondent Los Angeles County Department of Children and Family Services (DCFS) took custody of eight-year-old Mariah T. and her three-year-old brother Bryce T. after their father, Anthony T., reported that Mariah told him she had been sexually fondled by mother Monique B.'s live-in boyfriend Jason. [2] Mariah told a DCFS social worker that for two nights in a row Jason came into her room while she was sleeping, lay down next to her, and fondled her thigh near the crotch area. When she awoke and asked what was happening, Jason put his finger to his lips as a signal that she should keep quiet. Mariah told mother what happened, but mother accused her of lying and dismissed her claims. Mariah and Bryce also reported that mother had whipped them with a belt. According to father, Mariah told him that mother warned Mariah not to tell anyone what Jason had done and that, if she did, she would never see father again.

Based on this, DCFS filed a petition seeking to have the children declared dependents of the court under Welfare and Institutions Code section 300. [3] The petition alleged that the children suffered or were at risk of serious physical harm from mother's corporal punishment methods (§ 300, subd. (a)), and that Mariah had been sexually abused by a household member (§ 300, subd. (d)). The sexual abuse claims were also the basis of allegations that mother failed to protect the children from sexual abuse (§ 300, subd. (b)) and that mother's conduct placed Bryce at risk of sexual abuse (§ 300, subd. (j)). The corporal punishment claims also served as the basis of allegations that mother failed to adequately supervise or protect the children (§ 300, subd. (b)) and that the physical abuse of Bryce placed Mariah at risk of the same harm (§ 300, subd. (j)). [4]

At the jurisdictional hearing, Mariah testified that mother hit her in the back with a belt five times, once because she had lost her jacket. According to Mariah, one of those beatings left her with a red line on her back. Mariah testified that mother also used a belt on Bryce's stomach and hands on three occasions, once because he would not write out the letter 'B' and once because he sprayed mother's perfume in his own eye. Mariah recalled that one of those incidents left Bryce with marks on his hands that turned from yellow to purple or red. Mother also hit both children with her open hand several times. The court also considered a DCFS report where father stated he once found a large bruise on Bryce's forearm that was changing from purple to dark yellow.

As for the incidents with Jason, Mariah testified that on two nights in a row she woke up to find Jason in bed with her, touching her thigh through her clothes. She described Jason's hand as being near her crotch and said she felt uncomfortable and cried when these incidents happened because she believed Jason was trying to put his hand on her crotch. When Mariah told mother what happened, mother told her to stop lying. Father testified that when Mariah was finally able to tell him what had happened with Jason, she was hyperventilating and was so upset that she urinated on herself.

Mother admitted to hitting Mariah once on the buttocks with a belt and to once hitting Bryce's buttocks with a belt because he "was defying direct orders." Mother minimized the nature of her punishment methods and claimed father had engineered the accusations. In a pre-hearing DCFS report, mother told a social worker that Mariah was a compulsive liar, and at the hearing, mother denied that Mariah ever told her about the incidents with Jason.

The court said it believed Mariah and disbelieved mother and sustained the petition. At the later dispositional hearing, the court placed the children with father and ordered both visitation and reunification services for mother. Mother appeals from the jurisdictional and dispositional orders on the following grounds: (1) § 300, subdivision (a) is unconstitutionally vague; (2) there was insufficient evidence to support jurisdiction under any of the petition's allegations; and (3) there was insufficient evidence to support the dispositional order that took the children from her and placed them with father.

The dependency court took jurisdiction of Bryce and Mariah under section 300, subdivision (a), which applies if: "The child has suffered, or there is a substantial risk that the child will suffer, serious physical harm inflicted nonaccidentally upon the child by the child's parent or guardian. For the purposes of this subdivision, a court may find there is a substantial risk of serious future injury based on the manner in which a less serious injury was inflicted, a history of repeated inflictions of injuries on the child or the child's siblings, or a combination of these and other actions by the parent or guardian which indicate the child is at risk of serious physical harm. For purposes of this subdivision, 'serious physical harm' does not include reasonable and age-appropriate spanking to the buttocks where there is no evidence of serious physical injury." Mother contends subdivision (a) fails to properly define what constitutes serious physical harm, rendering it so vague that it violates her constitutional due process rights.

Under the due process provisions of both the federal constitution (U.S. Const., Amends.V, XIV) and the California Constitution (Cal. Const., art. I, § 7), parents in dependency proceedings are entitled to notice of the conduct prohibited by the dependency scheme. This means that the dependency statutes may not forbid or require conduct in terms so vague "`"that men of common intelligence must necessarily guess at its meaning and differ as to its application...,""' ( In re Alexander K. (1993) 14 Cal.App.4th 549, 558 , 18 Cal. Rptr.2d 22 (Alexander K.).)

As the parties point out, no published decision has considered whether section 300, subdivision (a) can withstand a constitutional void for vagueness challenge. [5] However, one decision of our Supreme Court at least suggests that it can. At issue in Williams v. Garcetti (1993) 5 Cal.4th 561 , 20 Cal.Rptr.2d 341 , 853 P.2d 507 (Williams ) was the constitutionality of an amendment to Penal Code section 272, which makes it a misdemeanor for parents to contribute to the delinquency of a minor under sections 601 and 602 or to the dependency of a minor under section 300. The amendment added language obligating parents to exercise reasonable care, supervision, protection, and control over their children and established a publicly funded parental diversion program. The plaintiffs were taxpayers who sued the Los Angeles County District Attorney to block enforcement of that amendment, contending that it created a new legal duty that was unconstitutionally vague. The trial court entered summary judgment for the defendant on the grounds that plaintiffs lacked standing and that the amendment was not unconstitutionally vague. The Court of Appeal reversed, but the Supreme Court reversed the appellate court and reinstated defendant's judgment.

The Williams court held that the amendment to Penal Code section 272 was not unconstitutionally vague because it incorporated the "definitions and the limits of parental duties that have long been a part of California dependency law and tort law." ( Williams, supra, 5 Cal.4th at p. 570 , 20 Cal.Rptr.2d 341 , 853 P.2d 507 .) Because the plaintiffs conceded that the statutory provisions relating to a child's welfare were sufficiently specific, the Williams court focused on the delinquency provisions of sections 601 and 602, concluding that those provisions were also sufficiently specific and made parents criminally liable only if they were criminally negligent in breaching their duties of parental control, supervision and care. In discussing plaintiffs' concession as to the child welfare obligations, the Williams court noted that parents' obligations to care for and protect their children were "well established and defined. For example, Welfare and Institutions Code section 300 contains a lengthy list of conditions under which a minor can be removed from the custody of a parent and declared a dependent child of the court. [Fn. omitted.] We agree with the Court of Appeal that section 300 provides guidelines sufficiently specific to delineate the circumstances under which a child will qualify for dependent status and thus to define the parental duty of care and protection that would prevent the recurrence of those circumstances." (Ibid.) In a footnote, the court summarized several subdivisions to section 300, including subdivision (a). (Id. at p. 570, fn. 6, 20 Cal.Rptr.2d 341 , 853 P.2d 507 .) Implicit in this statement is the notion that section 300, including subdivision (a), is sufficiently specific to satisfy due process. What Williams suggests we now hold to be so.

In determining whether a statute is unconstitutionally vague, only a reasonable certainty is required and a statute will be upheld if any reasonable and practical construction can be given to its language. ( Alexander K, supra, 14 Cal.App.4th at p. 558 , 18 Cal.Rptr.2d 22 .) There is a strong presumption in favor of upholding a statute unless its unconstitutionality "`"clearly, positively, and unmistakably appears."'" ( Williams, supra, 5 Cal.4th at p. 568 , 20 Cal.Rptr.2d 341 , 853 P.2d 507 .) Some imprecision in statutory language is allowable and a statute is not unconstitutionally vague if there is some matter of degree in the definition of a statutory term or the words used do not have a universally recognized meaning. Instead, a statute will be deemed sufficiently precise if its meaning can be fairly ascertained by references to similar statutes or other judicial determinations, or to the common law or the dictionary, or if the words have a common and generally accepted meaning. ( People v. Roberts (1981) 114 Cal.App.3d 960, 962-963 , 170 Cal.Rptr. 872 (Roberts) .)

Mother's strongest argument is based on section 300, subdivisions (c) and (e), which specify the level of harm that must occur in order to assume dependency court jurisdiction under those provisions. Subdivision (c) allows the court to take jurisdiction over children suffering "serious emotional damage," which is "evidenced by severe anxiety, depression, withdrawal, or untoward aggressive behavior toward self or others, as a result of the conduct of the parent or guardian...." Subdivision (e) allows the court to take jurisdiction of children under the age of five who have suffered severe physical abuse, which is defined as "any single act of abuse which causes physical trauma of sufficient severity that, if left untreated, would cause permanent physical disfigurement, permanent physical disability, or death; any single act of sexual abuse which causes significant bleeding, deep bruising, or significant external or internal swelling; or more than one act of physical abuse, each of which causes bleeding, deep bruising or intentional swelling, bone fracture, or unconsciousness; or the willful, prolonged failure to provide adequate food." Because subdivision (a) does not similarly define the types of physical harm that may be considered serious, mother contends there is no way for a parent to know whether their conduct has inflicted such harm, making the provision unconstitutionally vague.

We acknowledge the logic of mother's analysis, but believe there is another way to view this legislative omission and uphold section 300, subdivision (a): because the term "serious physical harm" has a sufficiently well-established meaning, no further statutory definition was required. The court in Alexander K., supra, 14 Cal. App.4th 549 , 18 Cal.Rptr.2d 22 , used this reasoning to affirm the constitutionality of section 300, subdivision (c) described above. Even though the provision specified the type of harm that would bring a child within its reach, it said nothing about the type of conduct that was prohibited. By looking to subdivision (j), which said that the intent of section 300 was to protect children from being abused, the court reasoned that subdivision (c) was designed to protect against abusive behavior. Based on this legislative intent and the dictionary definition of abuse, the court concluded that subdivision (c) was aimed at abusive behavior, not "run-of-the-mill flaws in our parenting styles," and that "[p]ersons of common intelligence would not have to guess whether someone was maltreating their children to the point of causing severe emotional harm." ( Alexander K, supra, at p. 559 , 18 Cal.Rptr.2d 22 .)

More to the point are decisions upholding the phrase "great bodily injury" against void for vagueness challenges. The court in People v. Maciel (2003) 113 Cal.App.4th 679 , 6 Cal.Rptr.3d 628 held that Penal Code section 422, the terrorist threats statute, was not unconstitutionally vague even though it criminalized threats to commit a crime which will result in great bodily injury. Noting that the term great bodily injury "`has been used in the law of California for over a century without further definition,'" the court said it was not a technical term that required further elaboration and, .standing alone, was not vague. (Id. at p. 686, 6 Cal. Rptr.3d 628 .) In Roberts, supra, 114 Cal. App.3d at pages 962-963, 170 Cal.Rptr. 872 , the court held that Penal Code section 245, subdivision (a), which applies to assaults likely to produce great bodily injury, was not unconstitutionally vague because the term "great bodily injury" was sufficiently certain. People v. Guest (1986) 181 Cal.App.3d 809 , 226 Cal.Rptr. 525 determined the constitutionality of Penal Code section 12022.7, which provides for a sentence enhancement to those who inflict great bodily injury in the commission or attempted commission of a felony, and which defines great bodily injury as "a significant or substantial physical injury." (Pen.Code, § 12022.7, subds.(a), (f).) Given the long-standing usage of the term "great bodily injury" in California, the court held it had not acquired a technical legal definition. "While the defendant may be correct in that an `I know it when I see it' standard is applied to injuries under [Penal Code] section 12022.7 [citation], men of common intelligence can apply these words of long usage to discern what injuries they are forbidden to inflict under pain of enhancement." ( People v. Guest, supra, at p. 812 , 226 Cal.Rptr. 525 .)

We do not view the phrase "serious physical harm" as being any less specific than the phrase "great bodily injury." Neither, apparently, does the United States Supreme Court. In James v. U.S. (2007) ___ U.S. ___, 127 S.Ct. 1586 , 167 L.Ed.2d 532 (James ), the court considered whether certain Florida state prior criminal convictions qualified for the enhanced sentence provided by the Armed Career Criminal Act ( 18 USC, § 924 (e)(1)), which applies, among others, to felonies that presented a "serious potential risk of physical injury." Addressing a point made in Justice Scalia's dissent, the majority rejected the notion that the phrase "serious potential risk of physical injury" was unconstitutionally vague because an ordinary person could not understand what conduct was prohibited. As proof, the court pointed to language in other state and federal statutes that it viewed as similar, including a federal statute that defined a terrorist act as conduct that "creates a substantial risk of serious bodily injury" as well as to a California statute (Health & Saf.Code, § 42.400.3, subd. (b)) that criminalized air pollution that "results in any unreasonable risk of great bodily injury...." ( James, supra, at pp. 1598-1599, fn. 6 .) We see little meaningful difference between the "substantial risk of serious bodily injury" referred to by the James court and the "substantial risk ... of serious physical harm" described by section 300, subdivision (a).

Finally, the court in Government of Virgin Islands v. Ayala (D.Virgin Islands 1993) 853 F.Supp. 160 , held that a criminal statute that applied to persons who placed a child in a situation where the child might suffer mental or emotional injury was unconstitutionally vague because it failed to specify the level of risk or harm required to fall within its terms (V.I.Code Ann., tit. 14, § 505 (Supp.1993)), and could therefore be applied to any injury, no matter how small. By contrast, however, the court pointed to an Arkansas statute (Ark.Code Ann., § 5-27-204) which applied to persons whose conduct created a "substantial risk of serious harm" to a child as one that would pass constitutional muster. ( Government of Virgin Islands v. Ayala, supra, at pp. 162-163.)

With these decisions in mind, we conclude that the term "serious physical harm" used in section 300, subdivision (a) is sufficiently certain. Although there may be an "I know it when I see it" component to this factual determination, as with the term "great bodily injury" we believe that parents of common intelligence can discern what injuries fall within its reach. ( People v. Guest, supra, 181 Cal.App.3d at p. 812 , 226 Cal.Rptr. 525 .)

Mother contends there is insufficient evidence to support the subdivision (a), (b), and (j) allegations that were based on physical injuries to the children because there is no evidence that she ever inflicted serious physical harm when she punished them. According to mother, evidence that she once left a red line on Mariah's back and once left purple and yellow marks on Bryce after hitting them with a belt does not show that the children suffered serious physical harm. Conceding for discussion's sake only that the line on Mariah's back did not amount to serious physical harm, we believe there was sufficient evidence that Bryce suffered serious physical harm.

The standard of proof at the jurisdictional stage of a dependency proceeding is a preponderance of the evidence, and we will affirm the court's findings if they are supported by substantial evidence. ( In re P.A. (2006) 144 Cal.App.4th 1339, 1344 , 51 Cal.Rptr.3d 448 .) Viewing the evidence under this standard, it appears that mother used a belt on a three-year-old child as punishment, striking him not on the buttocks, but on the stomach and forearms. On at least one occasion, this left Bryce with deep, purple bruises. In the context of a three year old, we hold that Bryce's injuries were serious enough for the court to assume jurisdiction under subdivision (a).

Even if there was not enough evidence to support jurisdiction of Mariah under subdivision (a), mother forgets that the subdivision (b) and (j) allegations were based on the substantial risk of future serious physical harm her conduct posed to both children. The evidence here showed a mother: who hit her three year old with a belt because he would not write out the letter `B' or because he sprayed perfume in his eyes, with one incident causing serious physical harm; who used a belt on her eight-year-old daughter on several occasions; who denied and minimized what she had done and attempted to justify it as legitimate corporal punishment; and who dismissed her daughter's claim of sex abuse by mother's boyfriend and threatened the girl that she would never see her father again if she told anyone about it. Based on this, a reasonable trier of fact was free to reject mother's claim that she would no longer use corporal punishment and could conclude that without intervention, the severity of punishment could escalate even further, increasing the risk to Bryce while placing Mariah at risk of serious harm, too. We therefore hold that there was sufficient evidence to assume jurisdiction of the children based on the physical abuse allegations.

The dependency court believed Mariah's claims that Jason had twice come to her bed and fondled her thigh and that mother accused her of lying about it. Based on that evidence, the court assumed jurisdiction of Mariah under section 300, subdivision (d) [child was sexually abused as defined in Penal Code section 11165.1 by household member and parent did not take reasonable steps to protect the child] and assumed jurisdiction of Bryce under section 300, subdivision (j) [child's sibling was abused as defined by other subdivisions, including (d), and there is substantial risk the child will be so abused as well].

Penal Code section 11165.1 defines sexual abuse as either sexual assault or sexual exploitation. Sexual assault means conduct violating any of several Penal Code sections including, as relevant here, lewd or lascivious acts on a child under Penal Code section 288. (Pen.Code, § 11165.1, subd. (a).) Sexual assault includes, among others, "[t]he intentional touching of the genitals or intimate parts (including the breasts, genital area, groin, inner thighs, and buttocks) or the clothing covering them, of a child ... for purposes of sexual arousal or gratification...." (Pen.Code, § 11165.;, subd. (b)(4).) Penal Code section 288 makes it a felony to commit lewd or lascivious acts on the body of a child under 14 "with the intent of arousing, appealing to, or gratifying the lust, passions, or sexual desires of that person or the child...."

Mother attacks the court's sex abuse findings on one ground only: there was no evidence that Jason touched Mariah with the specific intent of arousing or sexually gratifying either himself or Mariah. [6] As noted above, we will affirm the court's findings if they are supported by substantial evidence. ( In re P.A., supra, 144 Cal.App.4th at p. 1344 , 51 Cal.Rptr.3d 448 .) Because intent for purposes of Penal Code section 288 can seldom be proven by direct evidence, it may be inferred from the circumstances. ( People v. Mullens (2004) 119 Cal.App.4th 648, 662 , 14 Cal. Rptr.3d 534 (Mullens ).) As set forth below, we conclude there was sufficient evidence from the circumstances to infer that Jason acted with the requisite sexual intent.

The defendant in Mullens was charged with several violations of Penal Code section 288. At trial, the court allowed evidence of uncharged acts of lewd conduct on other young girls, including an incident where he supposedly caressed one girl's thigh as they lay together on a mattress. Mullens contended that evidence was inadmissible because there was no evidence of his sexual intent and therefore no proof that a violation of Penal Code section 288 occurred. The girl testified that she was 14 when the incident occurred, that she was clothed at the time, that Mullens hugged her closely and flirted with her, that there was some secrecy involved, and that she considered his conduct inappropriate. The appellate court held that if this evidence were believed, a reasonable jury could conclude that Mullens had acted with the requisite sexual intent. The facts here are similar. According to Mariah, she was clothed and asleep when Jason lay down next to her and fondled her thigh up high near her crotch. When she awoke, he signaled for her to remain quiet, from which an inference of guilty intent could be drawn. She felt uncomfortable and cried because she believed Jason was trying to touch her crotch. Jason came back the next night and repeated his conduct. Based on this, we believe it would be quite easy for a reasonable trier of fact to conclude that Jason acted with the requisite sexual intent.

The dependency court placed the children with father after finding by clear and convincing evidence that leaving them with mother created a substantial danger to their physical and emotional well-being and that there were no reasonable means to protect the children short of removing them from mother's custody. (§ 361, subd. (c).) Mother attacks this finding on two grounds: (1) there was no evidence to support any of the court's jurisdictional findings; and (2) the court should have pursued other alternatives, such as providing family maintenance services, prohibiting contact with Jason, or strictly supervising a "no corporal punishment" order. We reject the first contention because, as discussed above, there was sufficient evidence to support the court's jurisdictional findings. We reject the second contention because there was sufficient evidence to support a `finding that lesser alternatives to removal would not have worked.

In examining mother's claim, we review the record in the light most favorable to the dependency court's order to determine whether it contains sufficient evidence from which a reasonable trier of fact could make the necessary findings by clear and convincing evidence. ( In re Isayah C. (2004) 118 Cal.App.4th 684, 694-695 , 13 Cal.Rptr.3d 198 .) As to the sex abuse allegations, evidence supported a risk of continued sexual abuse would continue if Jason were to remain in mother's home. There is such evidence in the record. Before the children were detained, mother was given the option of having Jason move out so the children could remain with her, or having them placed outside the home. She chose the latter. Mother continued to deny that Jason had done anything wrong. A DCFS report prepared for the jurisdiction hearing showed that Jason continued to live in mother's home and at that hearing mother referred to Jason as her fiancee. Although a DCFS report prepared for the disposition hearing reported mother's claim that Jason had moved out on March 10, the report quoted mother as making the unlikely claim that she did not know Jason's new address and phone number. Mother also told the DCFS social worker that even though she was unsure whether she and Jason would continue their relationship, " we're going to appeal" the court's jurisdictional ruling. On this record, we hold that the dependency court could reasonably have concluded that Jason would remain in mother's home, thus placing the children at continued risk of sexual abuse. As a result, no reasonable alternatives to removal of custody from the mother were available.

Alternatively, mother did not raise the issue of whether Jason had left the home at either the jurisdictional or dispositional hearings and we therefore deem it waived. ( In re Aaron B. (1996) 46 Cal.App.4th 843, 846 , 54 Cal.Rptr.2d 27 .)

As to the allegations based on mother's use of a belt to punish the children, there was also sufficient evidence that lesser measures would not have worked. Mother had denied or minimized what she had done, refused to believe that Jason had fondled Mariah, and threatened to keep father away if Mariah told anyone what Jason did. The court was therefore free to reject mother's claim that she would no longer use corporal punishment, and could therefore find that removing the children from mother's custody was necessary on that ground as well.

For the reasons set forth above, the dependency court's jurisdictional and dispositional orders are affirmed.

WE CONCUR: COOPER, P.J., and FLIER, J.

[1] As is usual with dependency appeals, the facts and procedural history are lengthy and complex. We have narrowly tailored our statement of facts to fit the issues on appeal.

[2] Mother and father never married. They lived together for eight years until sometime in 2003, and agreed to share custody after their break-up.

[3] All further undesignated section references are to the Welfare and Institutions Code.

[4] We have described the allegations of the petition as amended by the dependency court on its own motion at the jurisdictional hearing.

[5] Alexander K., supra, 14 Cal.App.4th 549 , 18 Cal.Rptr.2d 22 , held that subdivision (c), which applies when a minor suffers severe emotional harm, was not unconstitutionally vague. We discuss Alexander K., post.

[6] Mother does not contend that even if jurisdiction were proper as to Mariah under section 300, subdivision (d), there was no evidence of a risk to Bryce under subdivision (j). (See In re P.A., supra, 144 Cal.App.4th at pp. 1345-1346, 51 Cal.Rptr.3d 448 , and cases cited therein, for circumstances under which the sibling of a sexually abused child might be at risk, including denial by the offending and non-offending parents that such abuse occurred.)